I have 2 statistics problems I am stuck on. Can anyone help me?
- Use the definition in Expression 3.13 to prove that $V(aX+b)=a^2\sigma_x^2$. [Hint: With $h(x)=aX+b$, $E[h(X)=a\mu+b$ where $\mu=E(X)$.] Expression 3.1 is:
$V(ax+b)=\sigma_{aX+b}^2=a^2\cdot\sigma_X^2$ And: $\sigma_{aX+b}=|a|\cdot\sigma_X.$
- Write a general rule for $E(X-c)$ where c is a constant. What happens when you let $c=\mu$, the expected value of $X$.
I can prove number #1 using the shortcut identity, but I don't think that's what it wants, I'm not sure where to start for #2.
Here's a strong hint for #2. Take a data set, then subtract (or add, even) the same number from each point. What happens to the mean? Try to experiment with specific values.